One illustrative method disclosed herein includes forming first and second FinFET devices in and above a first region and a second region of a semiconducting substrate, respectively, performing a first ion implantation process through a patterned mask layer to implant nitrogen into the second region, removing the patterned mask layer, performing a second ion implantation process to implant oxygen atoms into both the first and second regions, performing a heating process to form a layer of insulating material at least in the first region and performing at least one etching process to define at least one first fin in the first region and to define at least one second fin in the second region, the second fin being taller than the first fin.